My tank isn't 100% cycled yet, the nitrites are down to about .25ppm with ammonia at 0. I have had 6 head and tail light tetras in there from the beginning and they all seem to be doing fine. I was given 3 green tiger barbs 4 days ago that I added even though it hasn't fully cycled. I know that's really not the greatest of ideas, but I didn't realize that that low of a nitrite concentration would effect them this fast. Last night they all seemed fine and this morning one of them was having trouble maintaining his position in the water column and mostly swam in weak circles. Another was hanging out mostly near the surface and by now has also died. I have only 1 of the 3 left now, and although he is active currently he seems to be rapidly flushing water past his gills. Is he well on his way to dying as well? Kind of a bummer I didn't want to kill some fish as a result of my own stupidity! Is there anything I might be able to do to save him or is he probably a goner?

No, just don't gravel vac. Do the water change to sort of "water down" the nitrite and that's it. Beneficial bacteria is all in the gravel and on any hard surface in the tank, and of course in your filter.